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Setting Time when Tolerance is 5 Percent Calculator

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Second Order System Fundamental Parameters

✖Damping Ratio in control system is defined as the ratio with which any signal gets decayed.ⓘ Damping Ratio [ζ]			+10% -10%
✖Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.ⓘ Damped Natural Frequency [ω_d]			+10% -10%

✖Setting Time is the time required for a response to become steady.ⓘ Setting Time when Tolerance is 5 Percent [t_s]

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Setting Time when Tolerance is 5 Percent Solution

STEP 0: Pre-Calculation Summary

Formula Used

Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
t_s = 3/(ζ*ω_d)
This formula uses 3 Variables

Variables Used

Setting Time - (Measured in Second) - Setting Time is the time required for a response to become steady.
Damping Ratio - Damping Ratio in control system is defined as the ratio with which any signal gets decayed.
Damped Natural Frequency - (Measured in Hertz) - Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.

STEP 1: Convert Input(s) to Base Unit

Damping Ratio: 0.1 --> No Conversion Required
Damped Natural Frequency: 22.88 Hertz --> 22.88 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_s = 3/(ζ*ω_d) --> 3/(0.1*22.88)

Evaluating ... ...

t_s = 1.31118881118881

STEP 3: Convert Result to Output's Unit

1.31118881118881 Second --> No Conversion Required

FINAL ANSWER

1.31118881118881 ≈ 1.311189 Second <-- Setting Time

(Calculation completed in 00.006 seconds)

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National Institute of Information Technology (NIIT), Neemrana

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< Second Order System Calculators

Bandwidth Frequency given Damping Ratio

LaTeX Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

< Second Order System Calculators

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Rise Time given Damped Natural Frequency

LaTeX Go Rise Time = (pi-Phase Shift)/Damped Natural Frequency

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Peak Time

LaTeX Go Peak Time = pi/Damped Natural Frequency

< Control System Design Calculators

Bandwidth Frequency given Damping Ratio

LaTeX Go Bandwidth Frequency = Natural Frequency of Oscillation*(sqrt(1-(2*Damping Ratio^2))+sqrt(Damping Ratio^4-(4*Damping Ratio^2)+2))

First Peak Undershoot

LaTeX Go Peak Undershoot = e^(-(2*Damping Ratio*pi)/(sqrt(1-Damping Ratio^2)))

First Peak Overshoot

LaTeX Go Peak Overshoot = e^(-(pi*Damping Ratio)/(sqrt(1-Damping Ratio^2)))

Delay Time

LaTeX Go Delay Time = (1+(0.7*Damping Ratio))/Natural Frequency of Oscillation

Setting Time when Tolerance is 5 Percent Formula

LaTeX Go

Setting Time = 3/(Damping Ratio*Damped Natural Frequency)
t_s = 3/(ζ*ω_d)

What is setting time?

It is the time required for the response to reach the steady state and stay within the specified tolerance bands around the final value. In general, the tolerance bands are 2% and 5%. The settling time is denoted by ts.
The settling time for 5% tolerance band is -
ts=3/δωn

How to Calculate Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 Percent calculator uses Setting Time = 3/(Damping Ratio*Damped Natural Frequency) to calculate the Setting Time, Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value. Setting Time is denoted by t_s symbol.

How to calculate Setting Time when Tolerance is 5 Percent using this online calculator? To use this online calculator for Setting Time when Tolerance is 5 Percent, enter Damping Ratio (ζ) & Damped Natural Frequency (ω_d) and hit the calculate button. Here is how the Setting Time when Tolerance is 5 Percent calculation can be explained with given input values -> 1.311189 = 3/(0.1*22.88).

FAQ

What is Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value and is represented as t_s = 3/(ζ*ω_d) or Setting Time = 3/(Damping Ratio*Damped Natural Frequency). Damping Ratio in control system is defined as the ratio with which any signal gets decayed & Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.

How to calculate Setting Time when Tolerance is 5 Percent?

Setting Time when Tolerance is 5 percent is defined as the time required by the response to reach and steady with 5% of its final value is calculated using Setting Time = 3/(Damping Ratio*Damped Natural Frequency). To calculate Setting Time when Tolerance is 5 Percent, you need Damping Ratio (ζ) & Damped Natural Frequency (ω_d). With our tool, you need to enter the respective value for Damping Ratio & Damped Natural Frequency and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Setting Time?

In this formula, Setting Time uses Damping Ratio & Damped Natural Frequency. We can use 3 other way(s) to calculate the same, which is/are as follows -

Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)
Setting Time = 4/(Damping Ratio*Damped Natural Frequency)

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